Mathematical Problems In Linear Viscoelasticity
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Mathematical Problems In Linear Viscoelasticity
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Author : Mauro Fabrizio
language : en
Publisher: SIAM
Release Date : 1992-01-01
Mathematical Problems In Linear Viscoelasticity written by Mauro Fabrizio and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Science categories.
Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.
Boundary Value Problems In Linear Viscoelasticity
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Author : John M. Golden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Boundary Value Problems In Linear Viscoelasticity written by John M. Golden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
The classical theories of Linear Elasticity and Newtonian Fluids, though trium phantly elegant as mathematical structures, do not adequately describe the defor mation and flow of most real materials. Attempts to characterize the behaviour of real materials under the action of external forces gave rise to the science of Rheology. Early rheological studies isolated the phenomena now labelled as viscoelastic. Weber (1835, 1841), researching the behaviour of silk threats under load, noted an instantaneous extension, followed by a further extension over a long period of time. On removal of the load, the original length was eventually recovered. He also deduced that the phenomena of stress relaxation and damping of vibrations should occur. Later investigators showed that similar effects may be observed in other materials. The German school referred to these as "Elastische Nachwirkung" or "the elastic aftereffect" while the British school, including Lord Kelvin, spoke ofthe "viscosityofsolids". The universal adoption of the term "Viscoelasticity", intended to convey behaviour combining proper ties both of a viscous liquid and an elastic solid, is of recent origin, not being used for example by Love (1934), though Alfrey (1948) uses it in the context of polymers. The earliest attempts at mathematically modelling viscoelastic behaviour were those of Maxwell (1867) (actually in the context of his work on gases; he used this model for calculating the viscosity of a gas) and Meyer (1874).
Mathematical Problems In Viscoelasticity
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Author : Michael Renardy
language : en
Publisher: Longman Scientific and Technical
Release Date : 1987
Mathematical Problems In Viscoelasticity written by Michael Renardy and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Science categories.
Boundary Value Problems In Linear Viscoelasticity
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Author : John M. Golden
language : en
Publisher: Berlin : Springer-Verlag
Release Date : 1988
Boundary Value Problems In Linear Viscoelasticity written by John M. Golden and has been published by Berlin : Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Science categories.
The Theory Of Linear Viscoelasticity
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Author : D. R. Bland
language : en
Publisher: Courier Dover Publications
Release Date : 2016-10-05
The Theory Of Linear Viscoelasticity written by D. R. Bland and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-05 with Technology & Engineering categories.
This concise introduction to the concepts of viscoelasticity focuses on stress analysis. Three detailed sections present examples of stress-related problems, including sinusoidal oscillation problems, quasi-static problems, and dynamic problems. 1960 edition.
Creep And Relaxation Of Nonlinear Viscoelastic Materials
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Author : William N. Findley
language : en
Publisher: Courier Corporation
Release Date : 2013-01-15
Creep And Relaxation Of Nonlinear Viscoelastic Materials written by William N. Findley and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-15 with Technology & Engineering categories.
This pioneering book presents the basic theory, experimental methods, experimental results and solution of boundary value problems in a readable, useful way to designers as well as research workers and students. The mathematical background required has been kept to a minimum and supplemented by explanations where it has been necessary to introduce specialized mathematics. Also, appendices have been included to provide sufficient background in Laplace transforms and in step functions. Chapters 1 and 2 contain an introduction and historic review of creep. As an aid to the reader a background on stress, strain, and stress analysis is provided in Chapters 3 and 4, an introduction to linear viscoelasticity is found in Chapter 5 and linear viscoelastic stress analysis in Chapter 6. In the next six chapters the multiple integral representation of nonlinear creep and relaxation, and simplifications to single integral forms and incompressibility, are examined at length. After a consideration of other representations, general relations are derived, then expanded to components of stress or strain for special cases. Both constant stress (or strain) and variable states are described, together with methods of determining material constants. Conversion from creep to relaxation, effects of temperature and stress analysis problems in nonlinear materials are also treated here. Finally, Chapter 13 discusses experimental methods for creep and stress relaxation under combined stress. This chapter considers especially those experimental problems which must be solved properly when reliable experimental results of high precision are required. Six appendices present the necessary mathematical background, conversion tables, and more rigorous derivations than employed in the text. An extensive updated bibliography completes the book.
Stability In Viscoelasticity
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Author : A.D. Drozdov
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Stability In Viscoelasticity written by A.D. Drozdov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Mathematics categories.
The subject of stability problems for viscoelastic solids and elements of structures, with which this book is concerned, has been the focus of attention in the past three decades. This has been due to the wide inculcation of viscoelastic materials, especially polymers and plastics, in industry. Up-to-date studies in viscoelasticity are published partially in purely mathematical journals, partially in merely applied ones, and as a consequence, they remain unknown to many interested specialists. Stability in Viscoelasticity fills the gap between engineers and mathematicians and converges theoretical and applied directions of investigations. All chapters contain extensive bibliographies of both purely mathematical and engineering works on stability problems. The bibliography includes a number of works in Russian which are practically inaccessible to the Western reader.
Mathematical Analysis Of Viscoelastic Flows
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Author : Michael Renardy
language : en
Publisher: SIAM
Release Date : 2000-01-01
Mathematical Analysis Of Viscoelastic Flows written by Michael Renardy and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.
Crack And Contact Problems For Viscoelastic Bodies
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Author : G.A.C. Graham
language : en
Publisher: Springer
Release Date : 2014-05-04
Crack And Contact Problems For Viscoelastic Bodies written by G.A.C. Graham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Technology & Engineering categories.
The main emphasis of these Lecture Notes is on constructing solutions to specific viscoelastic boundary value problems; however properties of the equations of viscoelasticity that provide the theoretical underpinnings for constructing such solutions are also covered. Particular attention is paid to the solution of crack and contact problems. This work is of interest in the context of polymer fracture, modelling of material behaviour, rebound testing of polymers and the phenomenon of hysteretic friction.
Viscoelastic Solids 1998
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Author : Roderic S. Lakes
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Viscoelastic Solids 1998 written by Roderic S. Lakes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Technology & Engineering categories.
Viscoelastic Solids covers the mathematical theory of viscoelasticity and physical insights, causal mechanisms, and practical applications. The book: presents a development of the theory, addressing both transient and dynamic aspects as well as emphasizing linear viscoelasticity synthesizes the structure of the theory with the aim of developing physical insight illustrates the methods for the solution of stress analysis problems in viscoelastic objects explores experimental methods for the characterization of viscoelastic materials describes the phenomenology of viscoelasticity in a variety of materials, including polymers, metals, high damping alloys, rock, piezoelectric materials, cellular solids, dense composite materials, and biological materials analyzes high damping and extremely low damping provides the theory of viscoelastic composite materials, including examples of various types of structure and the relationships between structure and mechanical properties contains examples on the use of viscoelastic materials in preventing and alleviating human suffering Viscoelastic Solids also demonstrates the use of viscoelasticity for diverse applications, such as earplugs, gaskets, computer disks, satellite stability, medical diagnosis, injury prevention, vibration abatement, tire performance, sports, spacecraft explosions, and music.
